A small business tracks how advertising spending relates to weekly sales.
$\left(A\right)$ Plot Advertising Spending (x) vs Sales (y) & find the regression line & correlation coefficient.

• A. $y=20.587x+2015.6$; $0.971$
• B. $y=20.587x+2015.6$; $0.985$
• C. $y=24.373x$; $0.985$
• D. $y=24.373x$; $0.971$

Answer: (B)

Verified step by step guidance

1. Step 1: Organize the data by listing the advertising spending (x) and corresponding sales (y) for each week as given in the table.
2. Step 2: Calculate the means of the advertising spending (\(\bar{x}\)) and sales (\(\bar{y}\)) using the formulas: \(\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i\) and \(\bar{y} = \frac{1}{n} \sum_{i=1}^n y_i\), where \(n\) is the number of weeks.
3. Step 3: Compute the slope (\(b\)) of the regression line using the formula: \(b = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}\).
4. Step 4: Calculate the intercept (\(a\)) of the regression line using: \(a = \bar{y} - b \bar{x}\).
5. Step 5: Write the regression line equation as \(y = bx + a\). Then, calculate the correlation coefficient (\(r\)) using: \(r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}\) to measure the strength and direction of the linear relationship.